1. Cylindrical Lenses
Traditionally a cylindrical lens element is, as its name suggests, constituted by a cylinder of optical material such as glass. This type of lens is typically used in applications requiring magnification of an image in one dimension only. An example of this is transforming a point image into a line image or, put more generally, changing the height of an image without changing its width or vice versa. Typical industrial applications of a cylindrical lens include slit and line detector array illumination.
Although cylindrical lenses have a number of useful applications, they are more difficult and costly to manufacture than lenses with spherical surfaces. This is because the fine-grinding and polishing machines typically used in the manufacture of lenses are designed to work the surface of the lens randomly. This random working helps to ensure a smooth and geometrically correct surface and, at the same time, reduces the likelihood of scratches and other surface imperfections. Unfortunately though, a random wear function between two bounded surfaces generates a spherical and not a cylindrical surface and the typical tens grinding and polishing machines are, therefore, unsuitable for the manufacture of cylindrical lenses. Accordingly, specially designed machines are needed to generate and polish the cylindrical surfaces required for this type of lens and, as a result, the cost of cylindrical lenses is much greater than that associated with comparably sized spherical lenses.
In addition to the difficulties associated with their manufacture, traditionally formed cylindrical lenses, as with other lenses, can also cause chromatic and/or monochromatic aberrations in the images they form. Chromatic aberration, as discussed below, results from the fact that an optical material has a different refractive index for different wavelengths (colors) of light. Monochromatic aberrations, on the other hand, are caused by the physical configuration of the lens and can be classified into five categories, namely spherical aberration, coma, astigmatism, curvature of field and distortion.
2. GRIN Optical Materials
Over the past several years, optical materials with a gradient of refractive index, also known as GRIN materials, have been used in a variety of different applications in optics. Some GRIN lenses exhibit a change in refractive index along their optical axis, and are known as axially gradient GRIN lenses. Other types of GRIN lenses exhibit a change in refractive index along their radial axes orthogonal to the optical axis and are known as radially gradient GRIN lenses. More complex GRIN lenses, which have changes in refractive index in all three dimensions, are also known.
An example of a lens which has a chosen gradient in its index of refraction both orthogonal to and longitudinally along an optical axis is disclosed in U.S. Pat. No. 4,883,522 to Hagerty. Other examples of GRIN lenses can also be found in U.S. Pat. No. 4,929,065, also to Hagerty, which teaches a large change in the index of refraction over a significant dimension along its optical axis.
One advantage of using GRIN lenses is that they can be used in designing compound lens systems with a single, integral lens or a reduced number of lenses. Another advantage of GRIN lenses is their ability to reduce monochromatic aberrations. Generally, of the five different kinds of monochromatic aberrations (spherical aberration, coma, astigmatism, curvature of the field and distortion) a GRIN lens can substantially reduce spherical aberration, and to some extent also reduce the remaining four, particularly when compared with homogeneous lens systems.
However, GRIN lenses, just as homogeneous lenses, still exhibit chromatic aberration (caused by dispersion).
3. Chromatic Aberration
For all optical materials, whether homogeneous or GRIN, the refractive index (the amount light is bent by an optical material with respect to impinging light) varies based on the wavelength (or, conversely, the frequency) of the light. If the angle of incidence remains constant, different wavelengths of light, impinging on an optical material with the same angle of incidence, are bent differently.
For an homogeneous optical material, the refractive index for an impinging light with a short wavelength is always higher (i.e., bends more) than that for a light with a longer wavelength Thus, in a lens formed from an homogeneous optical material, blue light has shorter focal length than red light. This wavelength (or frequency) dependence of the refractive index is the cause for chromatic aberration in optical lenses.
Graphically, this is illustrated in FIG. 1, which shows a prior art lens 10 formed of homogeneous optical material. In order to focus light at a desired focal point, lens 10 has a curved surface as shown. However, as illustrated in FIG. 1, the focal length of the lens is shorter for impinging blue light 12 than for red light 14. Thus the blue light is focused at a focal point 16 while the red light is focused at a more distant focal point 18. As a result, the image formed by lens 10 experiences chromatic aberrations or dispersion.
More specifically, the dispersion of an optical material can generally be defined as a function of the difference in refractive index between a long-wavelength and a short-wavelength light impinging on the optical material. For an homogeneous material the dispersion is described by its Abbe number which is defined as: ##EQU1## where n.sub.d, n.sub.F and n.sub.C are the refractive indices of the optical material for yellow light, blue light and red light, having wavelengths, 587.6, 486.1, and 656.3 nm, respectively. The Abbe number and dispersion of an optical material are inversely related. Therefore, a lower dispersion means a higher Abbe number.
For most oxide homogeneous optical glass the Abbe number V.sub.d is in the range of 20 to 75. In order to obtain a higher Abbe number, exotic materials have been developed, such as fluoride glasses, which are undesirable because of high cost, toxicity, poor mechanical strength, poor resistance to staining, etc. In an homogeneous optical system, a number of lenses made of different glasses must be used to correct the chromatic aberration. The Fraunhofer doublet is an example of such an attempt.
The Fraunhofer doublet is a lens system formed of a crown double convex lens in contact with a concave-planar flint lens. The theoretical frequency invariant condition for this doublet is defined as: EQU f.sub.1d v.sub.1d +f.sub.2d v.sub.2d =0 (2)
where f.sub.1d, v.sub.1d, f.sub.2d and v.sub.2d are the focal length and Abbe number for the crown double convex lens an the concave-planar flint lens, respectively. Because the glasses used for the lens are homogeneous, the Abbe number remains a constant across the lens and Equation 2 holds true across the entire lens.
Unfortunately, the Fraunhofer lens system, cannot eliminate chromatic aberration completely and it often requires additional lenses, at a cost of a more complex system, to cancel out the dispersion. The Fraunhofer lens system also exhibits monochromatic aberrations inherent in homogeneous glass systems.
4. Dispersion in GRIN lenses
Even in GRIN lenses (which have many advantages over homogeneous lens systems), a desired dispersion characteristic is extremely difficult to produce. This is due, in part, to the complex dispersion properties of GRIN lenses. Through this specification, the terms "GRIN" and "gradient" have been used interchangeably.
For example, an axially gradient lens, has a variable refractive index along its optical axis. I.e., the index and Abbe number vary axially along the optical axis. As a result, it is extremely difficult to achieve desired dispersion properties with GRIN lenses.
Hence there is a need for an improved method of manufacture of a cylindrical lens as well as a method of manufacture of an optical GRIN lens in which the variables can be controlled to achieve a desired dispersion characteristic.